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Now, real batteries are constructed from materials which possess nonzero resistivities.
It follows that real batteries are not just pure voltage sources. They also possess
internal resistances.
Incidentally, a pure voltage
source is usually referred to as an emf (which stands for electromotive force). Of course,
emf is measured in units of volts.
A battery can be modeled as an emf connected in series with a resistor
, which represents its internal resistance. Suppose that such
a battery is used to drive a current through an external load resistor , as
shown in Fig. 17.
Note that in circuit diagrams an emf is represented as two closely spaced parallel
lines of unequal length. The electric potential of the longer line is greater than
that of the shorter one by volts. A resistor is represented as
a zigzag line.
Figure 17:
A battery of emf and internal resistance connected
to a load resistor of resistance .

Consider the battery in the figure. The voltage of the battery is
defined as the difference in electric potential between its positive and
negative terminals: i.e., the points and , respectively. As we move from to
, the electric potential increases by volts as we cross the
emf, but then decreases by volts as we cross the internal resistor.
The voltage drop across the resistor follows from Ohm's law, which implies that
the drop in voltage across a resistor , carrying a current
, is in the direction in which the
current flows. Thus, the voltage of the battery is related to its emf
and internal resistance via

(133) 
Now, we usually think of the emf of a battery as being essentially constant (since it
only depends on the chemical reaction going on inside the battery, which converts
chemical energy into electrical energy), so we must conclude that the voltage of a
battery actually decreases as the current drawn from it increases.
In fact, the voltage only equals the
emf when the current is negligibly small. The current draw
from the battery cannot normally exceed the critical value

(134) 
since
for the voltage becomes negative (which can only happen
if the load resistor is also negative: this is essentially impossible).
It follows that if we shortcircuit a battery, by connecting its
positive and negative terminals together using a conducting wire of negligible resistance,
the current drawn from the battery is limited by its internal resistance.
In fact, in this case, the current is equal to the maximum possible
current
.
A real battery is usually characterized in terms of
its emf (i.e., its
voltage at zero current), and the maximum current which it can supply.
For instance, a standard dry cell (i.e., the sort of
battery used to power calculators and torches) is usually rated at
and (say) . Thus, nothing really catastrophic is going to
happen if we shortcircuit a dry cell. We will run the battery down in a
comparatively short space of time, but no dangerously large current is going to
flow. On the other hand, a car battery is usually rated at
and something like (this is the sort of current needed to
operate a starter motor). It is clear that a car battery must have a much
lower internal resistance than a dry cell. It follows that if
we were foolish enough to shortcircuit a car battery the result would be
fairly catastrophic (imagine all of the energy needed to turn over the engine of
a car going into a thin wire connecting the battery terminals together).
Next: Resistors in Series and
Up: Electric Current
Previous: Resistance and Resistivity
Richard Fitzpatrick
20070714